Alumina bodies produced by conventional ceramic techniques have long been used as catalysts, catalyst supports, sorbents, and heat exchangers. Until the present invention however, it has been impractical to produce high purity alumina hollow bodies or bodies having concave surfaces or surfaces of complex shape, having high internal surface areas, because of the weakness of such bodies produced by normal ceramic processing techniques. In particular we refer to such bodies having wall thickness less than 1/16 inch and a radius of curvature greater than 1/8 inch.